My two cents: As to your first question:
What exactly happened here? Was Jesus angry at his mother...
The title "woman" may sound harsh, but it actually is a title of dignity, like madame
; it's what Christ used to address her from the Cross. Then there's "what have I to do with you?" This has also been taken to mean, "what does that have to do with you and me?" It ties into your second and third questions:
...did she commit a sin?
While St. John Chrysostom infamously wrote that the Theotokos sinned in a minor way through ambition--and other fathers like Origin and Basil the Great said she had sinned lightly through doubt while Christ was on the Cross--speculations about the Theotokos' sinfulness or sinlessness seem to be just that: speculation. We cannot even know for sure what our neighbor's heart's condition is; how much less can we know the heart of the one who is "more honorable than the Cherubim and more glorious beyond compare than the Seraphim"? The Theotokos is the holiest person who ever lived, and we know that, whatever the condition of her heart was, something special and unique was happening in her heart that had never happened before (and hasn't happened since) to a human being. I would advise you (though I wasn't asked and could be wrong on this) that you take the leading of the Blessed Augustine and, though you may have some wonderings about whether or not she sinned, to just let it go and not get too worked up over it.
Did He turn the water into wine out of respect toward His mother, or for some other reason?
It is interesting to note that, even though Christ says that His "hour has not yet come," he then turns around and does it. He did what His mother asked of Him. Again, He doesn't vocalize His reason, but it is a pleasant coincidence that her request moved Him to perform an action He didn't seem particularly "ready" to take.